In the text that follows, [xxx] signifies a footnote named "xxx" and
listed alphabetically at the end.
                                
Summary
-------
Cells is a mature, stable extension to CLOS[impl] allowing one to create classes 
whose instances can have slot values determined by instance-specific formulas. 

Example
-------
For example, in a text editor application we might have (condensed):

  (make-instance 'menu-item
	:label "Cut"
	:enabled (c? (bwhen (f (focus *window*))
			    (and (typep f 'text-widget)
				   (selection-range f)))))

Translated, the enabled state of the Cut menu item follows 
whether or not the user is focused on a text-edit widget and
whether they have in fact selected a range of text.

Meanwhile, the selection-range rule might be:

(let (start)
  (c? (if (mouse-down? .w.)
          (bwhen (c (mouse-pos-to-char self (mouse-pos .w.)))
            (if start
                (list start c)
              (setf start c)))
        (setf start nil))))

Now the only imperative code needed is some glue reading the OS event loop 
converting raw mouse down and mouse move events into window (the .w. symbol-macro)
attributes such as mouse-down? and mouse-pos. The desired functionality is achieved
by declarative rules which (like selection-range above) are entirely responsible for
deciding the selection range.

A final trick comes from slot observers. Suppose we are thinly wrapping a C GUI and need to
do something in the C library to actually make menu items available or not. 
It might look something like this:

 (defobserver enabled ((self menu-item) new-value old-value old-value-bound?)
     (menu-item-set (c-ptr self) (if new-value 1 0)))

ie, Some model attributes must be propagated outside the model as they change, and observers 
are callbacks we can provide to handle change.

Motivation
----------
As a child I watched my father toil at home for hours over paper 
spreadsheets with pencil and slide rule. After he changed one value, 
he had to propagate that change to other cells by first remembering 
which other ones included the changed cell in their computation. 
Then he had to do the calculations for those, erase, enter...
and then repeat that process to propagate those changes in a 
cascade across the paper.

VisiCalc let my father take the formula he had in mind and 
put it into (declare it to) the electronic spreadsheet. Then VisiCalc 
could do the tedious work: recalculating, knowing what to recalculate, 
and knowing in what order to recalculate.

Cells do for programmers what electronic spreadsheets did for my father.
Without Cells, CLOS slots are like cells of a paper spreadsheet. 
A single key-down event can cause a cascade of change throughout an 
application. The programmer has to arrange for it all to happen,
all in the right order: delete any selected text, insert 
the new character, re-wrap the text, update the undo mechanism, revisit
the menu statuses ("Cut" is no longer enabled), update the scroll bars,
possibly scroll the window, flag the file as unsaved... 

Here is a real-world case study:

"The last company I worked with made a product that was a control unit
for some mechanical devices, presenting both sensor readings coming in
from those devices and an interface to program the devices. Consider
it like a very sophisticated microwave oven, perhaps with a
temperature probe.

"The UI code was a frighteningly complex rat's nest. Input data
arriving from the sensors changed certain state values, which caused
the display to update, but the system state also changed, and rules
had to be evaluated, the outcome of which might be tuning to the
running job or warning messages presented to the user, and in the
meantime the user may be adjusting the running job. I'm sure there are
even more interactions I'm leaving out.

"There was no "large idea" in this code to organize these dependencies
or orchestrate the data flow. The individual facilities were
well-formed enough: "message" input and output, GUI widgets and forms,
real-world entities modeled as entities in the code. However, the
connections between these things were ad-hoc and not formalized. Every
change to the system would provoke defects, and the failure usually
involved not propagating some event, propagating it at the wrong time,
or propagating it to the wrong recipients."
   --- Steven Harris, on comp.lang.lisp

What Mr. Harris describes is what Fred Brooks [bullet] said was an essential
property of software development, meaning by essential that there was no
way around it, and thus his prediction that a software silver bullet was
in principle impossible.

Which brings us to Cells. See also [axiom] Phillip Eby's developing axiomatic 
definition he is developing in support of Ryan Forseth's SoC project. Mr. Eby was
inspired by his involvement to develop Trellis, his own Cells work-alike library
for Python.

DEFMODEL and Slot types
-----------------------
Classes, some of whose slots may be mediated by Cells, are defined by DEFMODEL, which is exactly
like DEFCLASS but adds support for two slot definition options, :cell and :unchanged-if. Classes 
defined by DEFMODEL can inherit from normal CLOS classes.

New slot definition options
----------------------------

   :cell {nil | t | :ephemeral}

:cell is optional. The default is ":cell t", meaning the Cells engine will manage the slot to give
it the spreadsheet-like characteristics. Specifying NIL signifies that this slot is entirely 
outside any handling by the Cells engine; it is just a plain CLOS slot. 

This next bit will not make sense until we have explained propagation of state change, but
specifying :ephemeral causes the Cells engine to reset the apparent slot 
value to NIL immediately and only after fully propagating any value assumed by the slot, either
by assignment to an input Cell (the vastly more common case) or by a rule calculation.

Ephemeral cells are necessary to correctly model events in the otherwise steady-state 
spreadsheet paradigm.

  :unchanged-if <function-name>

Specifying :unchanged-if is optional. [Come to think of it, it should be an error to specify
both :cell nil and :unchanged-if.] If specified, the named function is a predicate
of two arguments, the new and old value in that order. The predicate determines if a subsequent
slot value (either computed or assigned to an input) is unchanged in the sense that no propagation
is necessary, either to dependent ruled cells or (getting ahead of ourselves again) "on change" observers.
The default unchanged test is EQL.

Cell types
----------
The Cells library allows the programmer to specify at make-instance time that a Cell 
slot of an instance be mediated for the life of that instance by one of:

   -- a so-called "input" Cell;
   -- a "ruled" Cell; or
   -- no Cell at all.

Note that different instances of the same class may do different things Cells-wise with the same slot.
One label widget may have a fixed width of 42 and text "Hi, Mom!", where another might have
an input Cell mediating the text (so edit logic can assign new values as the user types) and a
rule mediating the width so the widget can have a minimum width of 42(so it does not disappear altogether)
yet grow based on text length and relevant font metrics to always leave room for one more character 
(if the GUI design calls for that).

To summarize, the class specification supplied with DEFMODEL specifies whether a slot can /ever/
be managed by the Cells engine. For those that can, at and only at instance initialization time
different instances can have different Cell types and rules specified to mediate the same slot.

Input Cells
-----------
A slot mediated by an input Cell may be assigned new values at runtime. These are how Cell-based models
get data from the world outside the model -- it cannot be rules all the way down. Typically, these
input assignements are made by code polling OS events via some GetNextEvent API call, or by callbacks
registered with an event system such as win32 WindowProc functions. Other code may poll sockets or 
serial inputs from an external device.

Ruled Cells
-----------
Ruled Cells come with an instance-specific  rule in the form of an anonymous function of two variables, 
the instance owning the slot and the prior value (if any) computed by the rule. These rules consist of 
arbitrarily complex Common Lisp code, and are invoked immediately after instance initialization (but see
the next bit on lazy cells).

When a rule runs, any dynamic read (either expressly in the rule source or during the execution of 
some function invoked by the rule) of a slot of any instance mediated by a Cell of any type establishes a
runtime dependency of the ruled cell on the slot of the instance that was read. Note then that thanks
to code branching, dependencies can vary after every rule invocation.

Lazy Ruled Cells
----------------
Laziness is cell-specific, applies only to ruled cells, and comes in four varieties:

     :once-asked -- this will get evaluated and "observed" on initialization, but then not get reevaluated 
immediately if dependencies change, rather only when read by application code.

     :until-asked  -- this does not get evaluated/observed until read by application code, but then it becomes 
un-lazy, eagerly reevaluated as soon as any dependency changes (not waiting until asked).

     :always -- not evaluated/observed until read, and not reevaluated until read after a dependency changes. 

Dataflow
--------
When application code assigns a new value to an input Cell (a quick way of saying an instance slot mediated by
an input Cell) -- typically by code polling OS events or a socket or an input device -- a cascade of recalculation
ensues to bring direct and indirect ruled dependents current with the new value assigned to the input Cell.

No Cell at All
--------------
Because of all that, it is an error to assign a new value to a slot of an instance not mediated by any Cell. 
The Cells engine can do a handy optimization by treating such slots as constants and not creating dependencies when ruled
Cells read these. But then we cannot let these Cells vary and still guarantee data integrity, because
we no longer know who else to update in light of such variation. The optimization, by the way, extends to
eliminating ruled Cells which, after any computation, end up not depending on any other cell.

Again, note that this is different from specifying ":cell nil" for some slot. Here, the Cells engine
has been told to manage some slot, but for some instance the slot has been authored to bear some value
for the lifetime of that instance.

Observers
---------
To allow the emergent animated data model to operate usefully on the world outside the model--if only to
update the screen--programmers may specify so-called observer callbacks dispatched according to: slot name, 
instance, new value, old value, and whether the old value actually existed (false only on the first go).
Observers are inherited according to the rules of CLOS class inheritance. If multiple primary observer
methods apply because of inheritance, they all get run, most specific last.

ie, observers are a GF with PROGN method combination.

Observers get called in two circumstances: as part of Model object initialization, in a processing step 
just after CLOS instance initialization, and when a slot changes value. Any observer of a Cell slot 
is guaranteed to be called at least once during intialization even if a cell slot is bound to a constant
or if it is an input or ruled Cell that never changes value.

It is legal for observer code to assign to input Cells, but (a) special syntax is required to defer execution
until the observed state change has fully propagated; and (b) doing so compromises the declarative
quality of an application -- one can no longer look to one rule to see how a slot (in this case the
input slot being assigned by the observer) gets its value. A reasonable usage might be one with
a cycle, where changing slot A requires a change to slot B, and changing slot B requires a change to
slot A, such as the scroll thumb position and the amount a document has been scrolled.

Finally, to make it possible for such a declarative model to talk intelligibly to imperative systems such as
Tcl/Tk which sometimes requires a precise sequence of commands for something to work at all, a mechanism exists by
which client code can (a) queue tasks for execution after a data change has fully propagated and (b) process
those tasks with a client-supplied handler. Tasks are queued with arbitrary keying data which can be used by 
the handler to sort or compress the queued tasks.

                                          
Data Integrity
--------------
When application code assigns to some input cell X, the Cells engine guarantees:

  - recomputation exactly once of all and only state affected by the change to X, directly or indirectly through 
    some intermediate datapoint. note that if A depends on B, and B depends on X, when B gets recalculated
    it may come up with the same value as before. In this case A is not considered to have been affected
    by the change to X and will not be recomputed.

  - recomputations, when they read other datapoints, must see only values current with the new value of X.
    Example: if A depends on B and X, and B depends on X, when X changes and A reads B and X to compute a
    new value, B must return a value recomputed from the new value of X.

  - similarly, client observer callbacks must see only values current with the new value of X; and

  - a corollary: should a client observer SETF a datapoint Y, all the above must
    happen with values current with not just X, but also with the value of Y /prior/
    to the change to Y.

  - Deferred "client" code must see only values current with X and not any values current with some
    subsequent change to Y queued by an observer

Benefits
--------
Program state guaranteed to be self-consistent, without programmer effort. Dependencies are identified
by the engine, and change propagation happens automatically.

Greater object re-use. Slots of instances can be authored with rules, not just literal values. In a sense,
we get greater reuse by allowing instances to override slot derivations instance by instance. But not slot
expressions, which are still class-oriented. By this I mean the observers expressing changes in value are 
dispatched by the class of the instance and so are not instance-specific. (Such a thing has been 
suggested, however.) Another strong bit of class-orientation comes from the fact that code reading
slot X of some instance Y obviously does so without knowing how the returned value was derived. It knows 
only that the slot is named X, and will do things with that value assuming only that it has the
X attribute of the instance Y. So again: the derivation of a slot value is potentially instance-oriented 
under Cells, but its expression or manifestation is still class-oriented.

Natural decomposition of overall application complexity into so many simple rules and slot observers. 
Let's return for a moment to VisiCalc and its descendants. In even the most complex financial spreadsheet  
model, no one cell rule accesses more than a relatively few other spreadsheet cells (counting a row or 
column range as one reference). Yet the complex model emerges. All the work of tracking dependencies
is handled by the spreadsheet software, which requires no special declaration by the modeller. They simply 
write the Cell rule. In writing the rule, they are concerned only with the derivation of one datapoint from
a population of other datapoints. No effort goes into arranging for the rule to get run at the right time,
and certainly no energy is spent worrying about what other cells might be using the authored cell. That
cell has certain semantics -- "account balance", perhaps -- and the modeller need only worry about writing
a correct, static computation of those semantics.

Same with Cells. :) The only difference is that VisiCalc has one "observer" requirement for all cells: 
update the screen. In Cells applications, a significant amount of application functionality -- indeed, all
its outputs -- end up in cell observers. But as discussed above, this additional burden falls only on 
the class designer when they decide to add a slot to a class. As instances are created and different rules
specified for different slots to achieve custom behavior, the effort is the same as for the VisiCalc user.

Model Building
--------------
Everything above could describe one instance of one class defined by DEFMODEL. A real application has 
multiple instances of multiple classes. So...

-- cells can depend on other cells from any other instance. Since a rule gets passed only "self", Cell users
need something like the Family class included with the Cells package effectively to turn a collection of
instances into a network searchable by name or type.

-- The overall model population must be maintainable by Cell slots such as the "kids" slot of the Family 
class. The burden here is on the Cells engine to allow one cell of one child to ask for the value of a cell of
another child and vice versa (with different Cells), when both children are the product of the same rule, 
or different rules when "cousins" are exchanging information. So we must gracefully traverse the parent/kids 
tree dispatching kids rules just in time to produce the other instance sought.

-- kid-slotting: used almost exclusively so far for orderly GUI layout, a parent must be able to specify 
rules for specific slots of kids. Example: a "stack" class wants to provide rules for child geometry
specifying left, right, or centered alignment and vertical stacking (with optional spacing) one below 
the other. The idea is that we want to author classes of what might be GUI subcomponents without worrying 
about how they will be arranged in some container.

-- finalization: when an instance appears in the "old kids" but not in the "new kids", a Cells engine
may need to arrange for all Cells to "unsubscribe" from their dependents. Cells takes care of that if
one calls "not-to-be" on an instance.


Suggested Applications
----------------------
Any application that must maintain an interesting, long-lived data model incorporating a stream of unpredictable 
data. Two examples: any GUI application and a RoboCup soccer client.

An application needing to shadow data between two systems. Examples: a Lisp GUI imlemented by thinly wrapping a 
C GUI library, where Lisp-land activity must be propagated to the C GUI, and C GUI events must propagate
to Lisp-land. See the Cells-Gtk or Celtk projects. Also, a persistent CLOS implementation that must echo 
CLOS instance data into, say, SQL tables.

Prior Art (in increasing order of priorness (age))
---------
Functional reactive programming:
  This looks to be the most active, current, and vibrant subset of folks working on this sort of stuff.
  Links:
   FlapJax (FRP-powered web apps) http://www.flapjax-lang.org/
   http://lambda-the-ultimate.org/node/1771
   http://www.haskell.org/frp/
   FrTime (scheme FRP implementation, no great links) http://pre.plt-scheme.org/plt/collects/frtime/doc.txt

Adobe Adam, originally developed only to manage complex GUIs. [Adam]

COSI, a class-based Cells-alike used at STSCI in software used to 
schedule Hubble telescope viewing time. [COSI]

Garnet's KR: http://www.cs.cmu.edu/~garnet/
Also written in Lisp. Cells looks  much like KR, though Cells was 
developed in ignorance of KR (or any other prior art). KR has 
an astonishing number of backdoors to its constraint
engine, none of which have turned out to be necessary for Cells.

The entire constraint programming field, beginning I guess with Guy Steele's
PhD Thesis in which he develops a constraint programming language or two:
  http://portal.acm.org/citation.cfm?id=889490&dl=ACM&coll=ACM
  http://www.cs.utk.edu/~bvz/quickplan.html

Flow-based programming, developed by J. Paul Morrison at IBM, 1971.
  http://en.wikipedia.org/wiki/Flow-based_programming

Sutherland, I. Sketchpad: A Man Machine Graphical Communication System. PhD thesis, MIT, 1963.
Steele himself cites Sketchpad as inexplicably unappreciated prior
art to his Constraints system:

See also:
 The spreadsheet paradigm: http://www.cs.utk.edu/~bvz/active-value-spreadsheet.html
 The dataflow paradigm: http://en.wikipedia.org/wiki/Dataflow
 Frame-based programming
 Definitive-programming

Commentary
----------
-- Jack Unrue, comp.lang.lisp
"Cells provides the plumbing for data dependency management which every 
non-trivial program must have; a developer using Cells can focus on 
computing program state and reacting to state changes, leaving Cells to worry about
how that state is propagated. Cells does this by enabling a declarative 
mechanism built via an extension to CLOS, and hence achieves its goal in a way 
that meshes well with with typical Common Lisp programming style."

-- Bill Clementson, http://bc.tech.coop/blog/030911.html
"Kenny Tilton has been talking about his Cells implementation on comp.lang.lisp 
for some time but I've only just had a look at it over the past few evenings. 
It's actually pretty neat. Kenny describes Cells as, conceptually, analogous to 
a spreadsheet cell (e.g. -- something in which you can put a value or a formula 
and have it updated automatically based on changes in other "cell" values). 
Another way of saying this might be that Cells allows you to define classes 
whose slots can be dynamically (and automatically) updated and for which 
standard observers can be defined that react to changes in those slots."

-- "What is Cells?", Cells-GTk FAQ, http://common-lisp.net/project/cells-gtk/faq.html#q2
"If you are at all familiar with developing  moderately complex software that 
is operated through a GUI, then you have probably 
learned this lesson: Keeping what is presented through the GUI in-sync with what 
the user is allowed to do, and in-sync with the computational state of the 
program is often tedious, complicated work. .... Cells-GTK helps 
with these tasks by providing an abstraction over the details; each of the tasks 
just listed can be controlled by (a) formula that specify the value of 
attributes of graphic features in the part-subpart declaration (that declaration 
is called 'defpart' in cells-gtk); and, (b) formula that specify the value of CLOS slots."

-- Phillip Eby, PyCells and peak.events, 
   http://www.eby-sarna.com/pipermail/peak/2006-May/002545.html
"What I discovered is quite cool.  The Cells system *automatically 
discovers* dynamic dependencies, without having to explicitly specify that 
X depends on Y, as long as X and Y are both implemented using cell 
objects.  The system knows when you are computing a value for X, and 
registers the fact that Y was read during this computation, thus allowing 
it to automatically invalidate the X calculation if Y changes....
Aside from the automatic dependency detection, the cells system has 
another trick that is able to significantly reduce the complexity of 
event cascades, similar to what I was trying (but failing) to do using 
the "scheduled thread" concept in peak.events.
Specifically, the cells system understands how to make event-based updates 
orderly and deterministic, in a way that peak.events cannot.  It 
effectively divides time into "propagation" and "non-propagation" 
states.  Instead of simply making callbacks whenever a computed value 
changes, the system makes orderly updates by queueing invalidated cells for 
updating.  Also, if you write code that sets a new value imperatively (as 
opposed to it being pulled declaratively), the actual set operation is 
deferred until all computed cells are up-to-date with the current state of 
the universe."

_____________
Uncommentary

-- Peter Seibel, comp.lang.lisp:
"I couldn't find anything that explained what [Cells] was and why I should care."

-- Alan Crowe, comp.lang.lisp:
"Further confession: I'm bluffing. I've grasped that Cells is
interesting, but I haven't downloaded it yet, and I haven't
checked out how it works or what /exactly/ it does."

_________                      
Footnotes

[Adam] "Adam is a modeling engine and declarative language for describing constraints and 
relationships on a collection of values, typically the parameters to an 
application command. When bound to a human interface (HI) Adam provides 
the logic that controls the HI behavior. Adam is similar in concept to a spreadsheet 
or a forms manager. Values are set and dependent values are recalculated. 
Adam provides facilities to resolve interrelated dependencies and to track 
those dependencies, beyond what a spreadsheet provides."
http://opensource.adobe.com/group__asl__overview.html#asl_overview_intro_to_adam_and_eve
________
[bullet] This resolves a problem Fred Brooks identified in 1987: ""The essence of a software 
entity is a construct of  interlocking concepts: data sets, relationships among data items, algorithms, 
and invocations of functions... Software systems have orders-of-magnitude more states than 
computers do...a scaling-up of a software  entity is not merely a repetition of the same elements 
in larger sizes; it is necessarily an increase in the number of different elements. In most cases, 
the elements interact with each other in some nonlinear fashion, and the complexity of the whole 
increases much more than linearly."
-- http://www.virtualschool.edu/mon/SoftwareEngineering/BrooksNoSilverBullet.html
______
[COSI] "The Constraint Sequencing Infrastructure (COSI) is an extension to
the Common Lisp Object System (*(CLOS)) which supports a constraint
based object-oriented programming model. .....

"A constraint is a specialized method which will be automatically
re-run by the COSI infrastructure whenever any of its input values
change. Input values are any of the object attributes that are
accessed by the constraint, and which are therefore assumed to
alter the processing within the constraint. 

"Whenever a state change occurs those constraints which depend upon
that state are added to a propagation queue. When the system is
queried a propagation cycle runs ensuring that the state of the
system is consistent with all constraints prior to returning a value."
-- http://www.cliki.net/ACL2/COSI?source
______
[impl] The Cells library as it stands is all about doing interesting things 
with slots of CLOS instances, but Cells is not only about CLOS or even Lisp. 
One Cells user is known to have mediated a global variable with a Cell, some work 
was done on having slots of DEFSTRUCTs mediated by Cells, and ports to C++, Java, and
Python have been explored.

_______
[axiom] Phillip Eby's axiomatic specification of Cells:

Data Pulse Axioms
=================

Overview: updates must be synchronous (all changed cells are updated at
once), consistent (no cell rule sees out of date values), and minimal (only
necessary rules run).

1. Global Update Counter:
   There is a global update counter. (Guarantees that there is a
globally-consistent notion of the "time" at which updates occur.)

2. Per-Cell "As Of" Value:
   Every cell has a "current-as-of" update count, that is initialized with
a value that is less than the global update count will ever be.

3. Out-of-dateness:
   A cell is out of date if its update count is lower than the update
count of any of the cells it depends on.

4. Out-of-date Before:
   When a rule-driven cell's value is queried, its rule is only run if the
cell is out of date; otherwise a cached previous value is
returned.  (Guarantees that a rule is not run unless its dependencies have
changed since the last time the rule was run.)

5. Up-to-date After:
   Once a cell's rule is run (or its value is changed, if it is an input
cell), its update count must be equal to the global update
count.  (Guarantees that a rule cannot run more than once per update.)

6. Inputs Move The System Forward
   When an input cell changes, it increments the global update count and
stores the new value in its own update count.


Dependency Discovery Axioms
===========================

Overview: cells automatically notice when other cells depend on them, then
notify them at most once if there is a change.


1. Thread-local "current rule cell":
   There is a thread-local variable that always contains the cell whose
rule is currently being evaluated in the corresponding thread.  This
variable can be empty (e.g. None).

2. "Currentness" Maintenance:
   While a cell rule's is being run, the variable described in #1 must be
set to point to the cell whose rule is being run.  When the rule is
finished, the variable must be restored to whatever value it had before the
rule began.  (Guarantees that cells will be able to tell who is asking for
their values.)

3. Dependency Creation:
   When a cell is read, it adds the "currently-being evaluated" cell as a
listener that it will notify of changes.

4. Dependency Creation Order:
   New listeners are added only *after* the cell being read has brought
itself up-to-date, and notified any *previous* listeners of the
change.  (Ensures that the listening cell does not receive redundant
notification if the listened-to cell has to be brought up-to-date first.)

5. Dependency Minimalism:
   A listener should only be added if it does not already present in the
cell's listener collection.  (This isn't strictly mandatory, the system
behavior will be correct but inefficient if this requirement isn't met.)

6. Dependency Removal:
   Just before a cell's rule is run, it must cease to be a listener for
any other cells.  (Guarantees that a dependency from a previous update
cannot trigger an unnecessary repeated calculation.)

7. Dependency Notification
   Whenever a cell's value changes (due to a rule change or input change),
it must notify all of its listeners that it has changed, in such a way that
*none* of the listeners are asked to recalculate their value until *all* of
the listeners have first been notified of the change.  (This guarantees
that inconsistent views cannot occur.)

7a. Deferred Recalculation
    The recalculation of listeners (not the notification of the listeners'
out-of-dateness) must be deferred if a cell's value is currently being
calculated.  As soon as there are no cells being calculated, the deferred
recalculations must occur.  (This guarantees that in the absence of
circular dependencies, no cell can ask for a value that's in the process of
being calculated.)

8. One-Time Notification Only
   A cell's listeners are removed from its listener collection as soon as
they have been notified.  In particular, the cell's collection of listeners
must be cleared *before* *any* of the listeners are asked to recalculate
themselves.  (This guarantees that listeners reinstated as a side effect of
recalculation will not get a duplicate notification in the current update,
or miss a notification in a future update.)

9. Conversion to Constant
   If a cell's rule is run and no dependencies were created, the cell must
become a "constant" cell, and do no further listener additions or
notification, once any necessary notifications to existing listeners are
completed.  (That is, if the rule's run changed the cell's value, it must
notify its existing listeners, but then the listener collection must be
cleared -- *again*, in addition to the clearing described in #8.)

10. No Changes During Notification:
   It is an error to change an input cell's value while change
notifications are taking place.

11. Weak Notification
   Automatically created inter-cell links must not inhibit garbage
collection of either cell.  (Technically optional, but very easy to do.)


